Having a pretty fun debate with a friend but neither of us can find much evidence from a solid website on this issue:

When a team puts a player on waivers to send them down to the minors, how does priority work.

I am of the belief that it goes worst record no matter the league until august, and then american league teams have priority on american league players and national league teams have priority on national league players.

Assuming the MLB 2008 rules are still valid, it looks like there are different priorities for trade waivers vs. other waivers. Trade assignment waivers claim priority is always by league. Other assignment waivers (outright, optional, or conditional release) claim priority doesn't take league into account.